In the present work, quasi-molecular compounds consisting of one antiproton (p̄) and one hydrogen-like ion are investigated: He + − p̄, Li 2+ − p̄, C 5+ − p̄, S 15+ − p̄, Kr 35+ − p̄, Ho 66+ − p̄, Re 74+ − p̄, U 91+ − p̄. For the calculations, the Dirac equation with two-centre potential is solved numerically using the dual-kinetically balanced finite-basis-set method adapted to systems with axial symmetry (A-DKB). Adiabatic potential curves are constructed for the ground state of the above quasi-molecular compounds in the framework of the A-DKB approach. Calculations were also performed for the case of an external magnetic field (the field is taken into account non-perturbatively). Zeeman shifts of the quasi-molecular terms are obtained for a homogeneous magnetic field with a strength of the laboratory order (up to 100 Tesla) directed along the axis of the molecule.